Methodology

CHAPTER 4: SPATIAL DISTRIBUTION OF EXTREME HEAT VULNERABILITY AND

4.2 Methodology

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include improved radiometric and spectral resolution, signal to noise ratio, refined bandwidth and two thermal infra-red bands (Karlson et al., 2015; Almutairi, 2015; Dube & Mutanga, 2015a). Furthermore, land cover classes generated from Landsat 8 have been shown to be more accurate than the previous Landsat series and MODIS data (Mwaniki et al., 2015; Yu, et al., 2013; Jia, et al., 2014; Ke, et al., 2015). Due to these improvements, studies have shown that Landsat 8 data enhances the retrieval of surface features such as biomass estimation, land cover mapping, discrimination of crops, and active fire and volcano detection (Dube & Mutanga, 2015a; Jia, et al., 2014; Banskota et al., 2014; Oumar, 2015; Han & Nelson, 2015; Kharat &

Musande, 2015; Blackett, 2014). Therefore, in this study, we hypothesize that the indices retrieved from Landsat 8 contain valuable information for characterization of landscapes useful for reliable urban heat vulnerability mapping.

The objective of this study was therefore to (i) include NDWI among the physical factors used for determining heat exposure, (ii) to produce a heat vulnerability map with spatial resolution greater than the resolution of socio-demographic vulnerability factors and (iii) use remote sensing physical variables obtained from the improved Landsat 8 optical and thermal data to map heat vulnerability of the highly heterogeneous Harare Metropolitan City during the hot season.

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and average household income. Each socio-demographic vulnerability factor was scaled between 0 and 1 with values increasing as vulnerability increased (Buscail, et al., 2012). The scaled socio-demographic factors were combined into a single social vulnerability layer using weighted sum by assigning equal importance to all the variables (Tomlinson, et al., 2011;

Buscail, et al., 2012). The resultant composite social vulnerability layer was converted from a vector to raster layer (Ho et al., 2015), resampled to the same properties as the 30 m bio- physical properties described below and scaled between 0 and 1 for further analysis (Tomlison et al., 2011).

Surface bio-physical exposure factors included density of buildings/imperviousness, bareness extent, vegetation abundance, and health as well as surface water content. The bio-physical factors were derived from remotely sensed 30 m NDVI, NDBI and NDWI. NDVI was used as a proxy for vegetation abundance and health, NDBI as a proxy for built- up/imperviousness/bareness extent and NDWI as a proxy for surface water content. The use of these indices was motivated by their high quantitative performance in discriminating surface properties, as well as ease of computation (Chen, et al., 2006; Gottshe & Olesen, 2001; Amiri, et al., 2009; Ma et al., 2010; Pu et al., 2006). These properties were selected due to their high correlation with land surface temperature which is well documented (Zhang, et al., 2009; Chen, et al., 2006; Pu, et al., 2006; Ma, et al., 2010; Song & Wu, 2015; Kerchove, et al., 2013; Essa, et al., 2013; Xu, et al., 2013). Studies have shown strong negative correlation between NDVI and NDWI with temperature (Steeneveld, et al., 2014; Chun & Guldmann, 2014). On the other hand, temperatures have been shown to increase with increasing density of buildings and imperviousness/bareness, thus high where NDBI is high (Srivanit et al., 2012; Yuan & Bauer, 2007; Essa, et al., 2013; Song & Wu, 2015; Chun & Guldmann, 2014). For example, Chen et al. (2006) observed that temperatures are high in areas of high building density. Combining NDVI and elevation has been reported to predict temperature better than each of the indices separately (Chen, et al., 2006; Maeda, 2015; Sobrino, et al., 2012). Therefore, combining these surface properties has the potential for adequately mapping risk of extreme surface temperatures. The land surface properties and digital to radiance conversion were obtained using the equations in Table 4.1 (Abegunde & Adedeji, 2015; Chen, et al., 2006; Xu, et al., 2013).

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Reducing vegetation fraction increases exposure of an area to high temperature except over water, while surface dryness and low altitude increases exposure of an area to high temperature.

An increase in the proportion of bare and built-up areas increases exposure of an area to high temperature (Chen et al., 2012). Temperature also decreases with surface wetness during the day (Steeneveld, et al., 2014; Chen, et al., 2006; Weng & Lu, 2008), therefore a low value of NDWI would increase vulnerability to high temperatures. Several studies have reported a decrease in temperature with increasing NDVI for values between -0.1 and 1, while temperature decreases as NDVI becomes more negative as it approaches -1 from -0.1 (Srivanit, et al., 2012; Cao, et al., 2008; Song & Wu, 2015). Water bodies have very low (negative) NDVI values and low daytime temperatures hence vulnerability was set to zero in these areas.

Therefore, in this study, vulnerability to high temperatures was set to decrease as NDVI increased from -0.1 to 1, as well as when it decreased to become more negative, from -0.1 to - 1. Each bio-physical vulnerability factor was scaled between 0 and 1 with values increasing as vulnerability increased.

66 Table 4.1: Selected vegetation indices

Function Equation References Normalized difference

built-up index

Normalized difference bareness index

𝑁𝐷𝐵𝐼 = 𝑑𝐵𝑎𝑛𝑑6−𝑑𝐵𝑎𝑛𝑑5

𝑑𝐵𝑎𝑛𝑑6+𝑑𝐵𝑎𝑛𝑑5 (Zha et al., 2003) 𝑁𝐷𝐵𝑎𝐼 = 𝑑𝐵𝑎𝑛𝑑6−𝑑𝐵𝑎𝑛𝑑10

𝑑𝐵𝑎𝑛𝑑6+𝑑𝐵𝑎𝑛𝑑10 (Zhao & Chen, 2005) Digital number (DN) to

radiance conversion

𝜌𝐵𝑎𝑛𝑑𝑛 = 𝑀_𝐿𝑑𝐵𝑎𝑛𝑑𝑛 + 𝐴_𝐿 (USGS, 2016)

Normalized difference

vegetation index 𝑁𝐷𝑉𝐼 =𝜌𝐵𝑎𝑛𝑑5−𝜌𝐵𝑎𝑛𝑑4

𝜌𝐵𝑎𝑛𝑑5+𝜌𝐵𝑎𝑛𝑑4 (Tucker, 1979) Normalized difference

water/wetness index 𝑁𝐷𝑊𝐼 = 𝜌𝐵𝑎𝑛𝑑5−𝜌𝐵𝑎𝑛𝑑6

𝜌𝐵𝑎𝑛𝑑5+𝜌𝐵𝑎𝑛𝑑6 (McFeeters, 1996)

dBandn represents 16 bit digital numbers of the n^th band of Landsat 8, ρBandn are the radiance values, ρBandn(max) is the maximum radiance, ρBandn(min) is the minimum radiance and dBandn(max) is the maximum digital number (65535) for the n^th band of Landsat 8. For each band ML

and AL for the conversion of DN to radiance are obtained from the metadata.

67 4.2.3 Vulnerability mapping

In vulnerability analysis, the variables are combined using overlay functions which include weighted sum and weighted average (Tomlinson, et al., 2011; Buscail, et al., 2012; Johnson, et al., 2014). However, the use of different weights based on relative importance of factors results in subjectivity of the vulnerability map produced, thus making the maps open to manipulation (Tomlinson et al., 2011). Therefore, the three scaled bio-physical vulnerability factors and the scaled composite social vulnerability layer were combined using weighted sum with all the factors assigned equal importance to produce the heat vulnerability. Tomlinson et al. (2011) and Buscail et al. (2012) also assigned equal importance to heat vulnerability to all considered factors. The weighted sum overlay function in ArcMap10.2 version was used to assign each of the four vulnerability factors a weight of 25%. The resultant heat vulnerability index layer was scaled between 0 and 1 and categorized using quantiles for presentation purpose. Similar to the categorization of heat vulnerability by Buscail et al. (2012), the lower 20% quantile was categorized as “Very low” vulnerability, the three intermediate quantiles as “Low”, “Moderate”

and “High” while the upper 20% quantile was categorized as “Very high” vulnerability.

4.2.4 Derivation of LST from thermal radiances

The Landsat 8 data contains two thermal bands, which enabled computation of temperature using the split window algorithm (Yang, Lin, et al., 2014; Qin, et al., 2001; McMillin, 1975;

Rozenstein, et al., 2014). The digital numbers of thermal data, Band 10 and Band 11 of Landsat 8, were converted to thermal radiance as described in Table 4.1. Brightness temperature (T10

and T11) were computed using Equation 4.1 with radiances derived from Bands 10 and 11 as input thermal layer.

𝑻_𝑵 = ^𝑲𝟐

𝑰𝒏(^𝑲𝟏

𝑳𝑵+𝟏) Equation 4.1

Where TN is the brightness temperature computed using thermal band N (10 or 11). Thermal conversion coefficients, K2 and K1, are constants obtained in the metadata file which accompanies the Landsat 8 images. Brightness temperature layers obtained were used in the split window algorithm land surface temperature derivation parameters in a procedure described in Qin et al. (2001) and Rozenstein et al. (2014). The general split-window algorithm for generating surface temperature (Ts) using two thermal bands takes the form:

𝑻_𝑺 = 𝑨_𝑶+ 𝑨_𝟏𝟎𝑻_𝟏𝟎+ 𝑨_𝟐𝑻_𝟏𝟏 Equation 4.2 Parameters A0, A1 and A2 are obtained using algorithms that combine atmospheric transmissivity with other parameters also provided and described by Rozenstein et al. (2014).

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Atmospheric transmissivity was derived from water vapour using an algorithm obtained from Qin et al (2001) and water vapour data at the time of image acquisition obtained from Aerosol Robotic Network (AERONET). The AERONET sun photometer data were previously recommended as a good source of water vapour data especially for daytime observations on cloud-free days (Yang, Lin, et al., 2014; Rozenstein, et al., 2014). Besides atmospheric transmittance, the algorithm for retrieving land surface temperature from two thermal bands of Landsat 8 developed by Rozenstein et al. (2014) also require land surface emissivity for each thermal band. Therefore, we retrieved pixel based spectral land surface emissivity for each thermal band using spectral radiance and blackbody radiance as developed by Yang et al.

(2004). Blackbody radiance was retrieved using Equation 4.3

𝝆𝑩𝒂𝒏𝒅𝒏(𝑩𝑩) = 𝝆𝑩𝒂𝒏𝒅𝒏(𝒎𝒊𝒏) + [𝝆𝑩𝒂𝒏𝒅𝒏(𝒎𝒂𝒙)− 𝝆𝑩𝒂𝒏𝒅𝒏(𝐦𝐢𝐧)][𝒅𝑩𝒂𝒏𝒅𝒏(𝒎𝒆𝒂𝒏)−𝒅𝑩𝒂𝒏𝒅𝒏(𝐦𝐢𝐧)]

𝟔𝟓𝟓𝟑𝟓

Equation 4.3 Yang, et al. (2004) obtained better blackbody emissivity values using dBandn(mean) than using 65535 hence the choice for use in this study. Land surface emissivity for each thermal band was computed using Equation 4.4

𝑳𝑺𝑬 = ^{𝒅𝑩𝒂𝒏𝒅𝒏}

𝒅𝑩𝒂𝒏𝒅𝒏(𝑩𝑩) Equation 4.4

Where dBandn(mean) is the average of the maximum digital number for scene and 65535 while the other variables are defined in Table 1. Land surface emissivity maps were used in Equation together with other parameters described above to retrieve land surface temperature. Land surface temperature was calculated using the brightness temperature layers using Equation 2.

Furthermore, we performed a spatial correlation between the mapped heat vulnerability and observed distribution of land surface temperatures.